An example of a turbine blade according to the prior art is shown in FIGS. 1 and 2 of the accompanying drawings. The turbine blade 1 has a blade body or airfoil 2 extending from an outer platform 3 to an inner platform 4. The airfoil 2 is hollow and receives a gaseous coolant (e.g. air), which is discharged from holes 6 in the trailing edge 7. The interior of the airfoil 2 also communicates with the pressure side 8 and suction side 9 of the airfoil through rows of film cooling holes 11 so that the outside of the airfoil is cooled by a film which forms on the surface. Similar rows of holes 12 are formed in the platforms 3, 4. The turbine blade 1 is made by casting and there is a smooth transition or fillet 13 between each of the pressure and suction sides 8, 9 of the airfoil 2 and each of the platforms 3, 4.
For efficient cooling of the fillets 13, groups 14 of film cooling holes are provided at several different positions at the fillet. However, these additional holes increase the amount of gaseous coolant which has to be supplied to the turbine blade 1.